Question of the week - 35 (A writer gets paid $10 per page, for .....)

Solution

Given
In this question, we are given that

• A writer gets paid $10 per page, for the first 40 pages that she writes on a day.
• For every additional page that she writes on that day, she gets an extra $4 per page over the normal pay per page.
• She writes at least 35 pages in a single day.
• In a span of 3 consecutive days, she earned a total amount of $1500.

To Find
From the given information, we need to determine

• The maximum number of pages that the writer wrote in a single day

Approach & Working
As we are trying to find the maximum number of pages that she wrote in a single day, we need to minimize the number of pages that she wrote on the other 2 days.

It is also given that the writer wrote at least 35 pages on a single day.

• Hence, we can assume that the other 2 days she wrote 35 pages each day and earned (35 x 2 x $10) = $700 in total.
• Therefore, her earning on the day she writes maximum pages = ($1500 – $700) = $800

Now, for the first 40 pages, she is already earning ($10 x 40) = $400.
So, for the remaining pages she can earn = $800 – $400 = $400.

As in every extra page beyond 40 pages, she is earning ($10 + $4) = $14, then number of extra pages she wrote should be $400/14 = 28.57, which is not an integer!
It means, she must have written a few pages on the other 2 days.

• If she wrote 1 page on the other 2 days, then on that day she wrote ($400 - $10)/$14 = 27.8, which is not an integer.
• If she wrote 2 pages on the other 2 days, then on that day she wrote ($400 - $20)/$14 = 27.1, which is not an integer.
• If she wrote 3 pages on the other 2 days, then on that day she wrote ($400 - $30)/$14 = 26.4, which is not an integer.
• If she wrote 4 pages on the other 2 days, then on that day she wrote ($400 - $40)/$14 = 25.7, which is not an integer.
• If she wrote 5 pages on the other 2 days, then on that day she wrote ($400 - $10)/$14 = 25, which is an integer.

Therefore, she must have written 25 extra pages on that day, and hence, the total number of pages that she wrote is 40 + 25 = 65

Hence, the correct answer choice is option C.

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